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Lecturer(s)
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Jukl Marek, doc. RNDr. Ph.D.
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Juklová Lenka, RNDr. Ph.D.
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Course content
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1. Quadratic and bilinear forms, polar bases, signatures. 2. Diagonalisation of the matrix of a real quadratic form. 3. Conics in the Euclidean plane. Canonical equations. 4. Lines and conics. 5. Metric and affine classification of conics, affine and metric invariants. 6. Quadratic surfaces in a 3-dimmensional Euclidean space (quadrics). Canonical equations. 7. Lines and quadrics. Planes and quadrics. 8. Metric and affine classification of quadrics.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
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Learning outcomes
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Understand the analytic geometry of conics and quadrics in Euclidean plane resp. 3-dimensional space. To master corresponding tasks.
1. Knowledge Students describe elements of coordinated geometry of quadrics in euclidean plane and 3-dimensional space and define relations between quadrics and other geometrical configurations.
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Prerequisites
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unspecified
KAG/ALG1 and KAG/GEO1
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Assessment methods and criteria
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Oral exam, Written exam, Student performance
Credit: the student has to participate actively in seminars and pass a written test. Exam: the student has to understand the subject and be able to prove the principal results. The student has to be able to solve problems.
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Recommended literature
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Sekanina M. (1986). Geometrie I. SPN Praha.
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Berger, M. (2004). Geometry I, II. Universitext Springer-Verlag Berlin.
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Hejný M. (1985). Geometria I. SPN Bratislava.
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JUKL Marek. (2014). Analytická geometrie. Olomouc.
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Marková L. (1991). Cvičení z geometrie I. VUP Olomouc.
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Zlatoš P. (2011). Lineárna algebra a geometria. Marenčin Bratislava.
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